On a damped Szego equation (with an appendix in collaboration with Christian Klein)
Analysis of PDEs
2019-12-24 v1 Classical Analysis and ODEs
Abstract
We investigate how damping the lowest Fourier mode modifies the dynamics of the cubic Szeg{\"o} equation. We show that there is a nonempty open subset of initial data generating trajec-tories with high Sobolev norms tending to infinity. In addition, we give a complete picture of this phenomenon on a reduced phase space of dimension 6. An appendix is devoted to numerical simulations supporting the generalisation of this picture to more general initial data.
Keywords
Cite
@article{arxiv.1912.10933,
title = {On a damped Szego equation (with an appendix in collaboration with Christian Klein)},
author = {Patrick Gerard and Sandrine Grellier},
journal= {arXiv preprint arXiv:1912.10933},
year = {2019}
}